Question 926525: In 1999 there were 4076 grocery stores and in 2003 there were 1078 grocery stores. Assuming the trend has and will continue to follow a linear pattern. Predict the number of grocery stores there were in the year 2008? (Let t=9 represent 1999)
Answer by EMStelley(208)   (Show Source):
You can put this solution on YOUR website! In this problem we are going to need to create a linear equation that predicts the number of grocery stores so that we can predict the number in 2008. In the problem they gave us our independent variable, which is time t, and said to let t=9 represent 1999. Then we can call the number of grocery stores g. Then the information "In 1999 there were 4076 grocery stores" can be written as an ordered pair (t,g) as (9,4076). And the other piece "in 2003 there were 1078 grocery stores" can be written as (13,1078). We obtained the number 13 for t by noting that t=9 represents 1999 and 2003 is 4 years after that.
Now that we have two points we can find the slope.
 =  = 
Now that we have slope, we can find the equation by using point-slope form with the slope we just found and one of the points (I will use the first one):
Now let's solve for g.
So, the question is asking to predict the number of grocery stores in 2008. We must start by finding the correct value for t. Since t = 9 in 1999 and 2008 is 9 years later, our t value here is 18. So we will use the above equation and plug in 18 for t.
Now, obviously we cannot have a negative number of grocery stores, so the only logical answer here is 0. By the time 2008 rolls around, according to the trend laid out in this problem, there will be no more grocery stores.
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